Kalman-filter control schemes for fringe tracking. Development and application to VLTI/GRAVITY

The implementation of fringe tracking for optical interferometers is inevitable when optimal exploitation of the instrumental capacities is desired. Fringe tracking allows continuous fringe observation, considerably increasing the sensitivity of the interferometric system. In addition to the correction of atmospheric path-length differences, a decent control algorithm should correct for disturbances introduced by instrumental vibrations, and deal with other errors propagating in the optical trains. We attempt to construct control schemes based on Kalman filters. Kalman filtering is an optimal data processing algorithm for tracking and correcting a system on which observations are performed. As a direct application, control schemes are designed for GRAVITY, a future four-telescope near-infrared beam combiner for the Very Large Telescope Interferometer (VLTI). We base our study on recent work in adaptive-optics control. The technique is to describe perturbations of fringe phases in terms of an a priori model. The model allows us to optimize the tracking of fringes, in that it is adapted to the prevailing perturbations. Since the model is of a parametric nature, a parameter identification needs to be included. Different possibilities exist to generalize to the four-telescope fringe tracking that is useful for GRAVITY. On the basis of a two-telescope Kalman-filtering control algorithm, a set of two properly working control algorithms for four-telescope fringe tracking is constructed. The control schemes are designed to take into account flux problems and low-signal baselines. First simulations of the fringe-tracking process indicate that the defined schemes meet the requirements for GRAVITY and allow us to distinguish in performance. In a future paper, we will compare the performances of classical fringe tracking to our Kalman-filter control.Comment: 17 pages, 8 figures, accepted for publication in A&

Non Co-Operative Detection of LPI/LPD Signals Via Cyclic Spectral Analysis

This research proposes and evaluates a novel technique for detecting LPI/LPD communication signals using a digital receiver primarily designed to detect radar signals, such as a Radar Warning Receiver (RWR) or an Electronic Support Measures (ESM) receiver. The proposed Cyclic Spectrum Analysis (CSA) receiver is a robust detector that takes advantage of the spectral correlation properties of second-order cyclostationary signals. A computationally efficient algorithm is used to estimate the Spectral Correlation Function (SCF). Using state-of-the-art FFT processing, it is expected that the proposed CSA receiver architecture could estimate the entire cyclic spectrum m approximately 0.6 ms. The estimate is then reduced to an energy related test statistic that is valid for all cycle frequencies within the receiver bandwidth. By producing an estimate of the cyclic spectrum, the CSA receiver also benefits post-detection tasks such as signal classification and exploitation. As modeled, the ideal CSA receiver detection performance is within 1.0 dB of the radiometer in benign signal environments and consistently outperforms the radiometer in adverse signal environments. The effect on detection performance when the CSA receiver is implemented with channelized and quadrature digital receiver architectures is also examined

Methods for Focal Plane Array Resolution Estimation Using Random Laser Speckle in Non-paraxial Geometries

The infrared (IR) imaging community has a need for direct IR detector evaluation due to the continued demand for small pixel pitch detectors, the emergence of strained-layer-super-lattice devices, and the associated lateral carrier diffusion issues. Conventional laser speckle-based modulation transfer function (MTF) estimation is dependent on Fresnel propagation and a wide-sense-stationary input random process, limiting the use of this approach for lambda (wavelength)-scale IR devices. This dissertation develops two alternative methodologies for speckle-based resolution evaluation of IR focal plane arrays (FPAs). Both techniques are formulated using Rayleigh-Sommerfield electric field propagation, making them valid in the non-paraxial geometries dictated for resolution estimation of lambda-scale devices. The generalized FPA MTF estimation approach numerically evaluates Rayleigh-Sommerfeld speckle irradiance autocorrelation functions (ACFs) to indirectly compute the power spectral density (PSD) of a non-wide-sense-stationary (WSS) speckle irradiance random process. The experimental error incurred by making WSS assumptions regarding the associated laser speckle random process is quantified utilizing the Wigner distribution function. This method is experimentally demonstrated on a lambda-scale longwave IR FPA, showing a 27% spatial frequency range improvement over established estimation methodology. Additionally, a resolution estimation approach, which utilizes an iterative maximum likelihood estimation approach and speckle irradiance ACFs to solve for a system impulse response, is developed and demonstrated with simulated speckle imagery

Detection and classification of frequency-hopped spread spectrum signals

This dissertation proposes a means of defeating Frequency-Hopped (FH) spread spectrum modulation using an intercept receiver capable of fast emission detection and classification. By continuously analyzing the spectrum and classifying detected emissions, the receiver is capable of following a FH signal as it changes frequency. No a priori knowledge of the FH signals is needed by the receiver;The basic structure used for emission detection is the radiometer. The tradeoffs between integration time and detection bandwidth examined. A suitable design for the intercept receiver is selected, and a digital architecture using Fast Fourier Transforms (FFT\u27s) to implement the radiometer function is proposed. The detection performance of the digital receiver is predicted and compared with conventional analog radiometric receivers. Constraints on the time-bandwidth product imposed by the use of FFT\u27s are also examined;Correct emission classification is the second problem that must be addressed before signal interception is possible. Two classification algorithms developed using Baysian decision theory are discussed. The algorithms use data with arbitrary distributions calculated from samples of detected emissions to classify emissions. The first classification algorithm considered is the well-known maximum likelihood rule. The form of the decision rule, and the classification accuracy that can be expected from it are discussed. The epoch classification algorithm is then developed to eliminate errors which occur using the maximum likelihood classification algorithm. The probability of classification error for the epoch classification algorithm is found to be considerably less than that obtained using maximum likelihood classification;To illustrate the application of the classification algorithms, emission frequency is used with hop frequency order statistics to classify emissions. The use of emission frequency is shown to eliminate or significantly reduce the probability of classification error when hopping spans from different FH signals are distinct or only partially overlap

Detecting Reflected Light from Close-In Extrasolar Giant Planets with the Kepler Photometer

NASA's Kepler Mission promises to detect transiting Earth-sized planets in the habitable zones of solar-like stars. In addition, it will be poised to detect the reflected light component from close-in extrasolar giant planets (CEGPs) similar to 51 Peg b. Here we use the DIARAD/SOHO time series along with models for the reflected light signatures of CEGPs to evaluate Kepler's ability to detect such planets. We examine the detectability as a function of stellar brightness, stellar rotation period, planetary orbital inclination angle, and planetary orbital period, and then estimate the total number of CEGPs that Kepler will detect over its four year mission. The analysis shows that intrinsic stellar variability of solar-like stars is a major obstacle to detecting the reflected light from CEGPs. Monte Carlo trials are used to estimate the detection threshold required to limit the total number of expected false alarms to no more than one for a survey of 100,000 stellar light curves. Kepler will likely detect 100-760 51 Peg b-like planets by reflected light with orbital periods up to 7 days.Comment: 43 pages, 6 figures, 9 tables, accepted for publication by ApJ May 200

Statistical Properties and Applications of Empirical Mode Decomposition

Signal analysis is key to extracting information buried in noise. The decomposition of signal is a data analysis tool for determining the underlying physical components of a processed data set. However, conventional signal decomposition approaches such as wavelet analysis, Wagner-Ville, and various short-time Fourier spectrograms are inadequate to process real world signals. Moreover, most of the given techniques require \emph{a prior} knowledge of the processed signal, to select the proper decomposition basis, which makes them improper for a wide range of practical applications. Empirical Mode Decomposition (EMD) is a non-parametric and adaptive basis driver that is capable of breaking-down non-linear, non-stationary signals into an intrinsic and finite components called Intrinsic Mode Functions (IMF). In addition, EMD approximates a dyadic filter that isolates high frequency components, e.g. noise, in higher index IMFs. Despite of being widely used in different applications, EMD is an ad hoc solution. The adaptive performance of EMD comes at the expense of formulating a theoretical base. Therefore, numerical analysis is usually adopted in literature to interpret the behavior. This dissertation involves investigating statistical properties of EMD and utilizing the outcome to enhance the performance of signal de-noising and spectrum sensing systems. The novel contributions can be broadly summarized in three categories: a statistical analysis of the probability distributions of the IMFs and a suggestion of Generalized Gaussian distribution (GGD) as a best fit distribution; a de-noising scheme based on a null-hypothesis of IMFs utilizing the unique filter behavior of EMD; and a novel noise estimation approach that is used to shift semi-blind spectrum sensing techniques into fully-blind ones based on the first IMF. These contributions are justified statistically and analytically and include comparison with other state of art techniques

Detecting and locating electronic devices using their unintended electromagnetic emissions

Electronically-initiated explosives can have unintended electromagnetic emissions which propagate through walls and sealed containers. These emissions, if properly characterized, enable the prompt and accurate detection of explosive threats. The following dissertation develops and evaluates techniques for detecting and locating common electronic initiators. The unintended emissions of radio receivers and microcontrollers are analyzed. These emissions are low-power radio signals that result from the device\u27s normal operation. In the first section, it is demonstrated that arbitrary signals can be injected into a radio receiver\u27s unintended emissions using a relatively weak stimulation signal. This effect is called stimulated emissions. The performance of stimulated emissions is compared to passive detection techniques. The novel technique offers a 5 to 10 dB sensitivity improvement over passive methods for detecting radio receivers. The second section develops a radar-like technique for accurately locating radio receivers. The radar utilizes the stimulated emissions technique with wideband signals. A radar-like system is designed and implemented in hardware. Its accuracy tested in a noisy, multipath-rich, indoor environment. The proposed radar can locate superheterodyne radio receivers with a root mean square position error less than 5 meters when the SNR is 15 dB or above. In the third section, an analytic model is developed for the unintended emissions of microcontrollers. It is demonstrated that these emissions consist of a periodic train of impulses. Measurements of an 8051 microcontroller validate this model. The model is used to evaluate the noise performance of several existing algorithms. Results indicate that the pitch estimation techniques have a 4 dB sensitivity improvement over epoch folding algorithms --Abstract, page iii